On Functional Representations of Positive Hilbert Space Operators
In this paper we consider some faithful representations of positive Hilbert space operators on structures of nonnegative real functions defined on the unit sphere of the Hilbert space in question. Those representations turn order relations between positive operators to order relations between real f...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2021
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| Sorozat: | INTEGRAL EQUATIONS AND OPERATOR THEORY
93 No. 1 |
| Tárgyszavak: | |
| doi: | 10.1007/s00020-020-02605-5 |
| mtmt: | 31862557 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37372 |
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| 008 | 250804s2021 hu o 000 eng d | ||
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| 024 | 7 | |a 10.1007/s00020-020-02605-5 |2 doi | |
| 024 | 7 | |a 31862557 |2 mtmt | |
| 040 | |a SZTE Publicatio Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Molnár Lajos | |
| 245 | 1 | 3 | |a On Functional Representations of Positive Hilbert Space Operators |h [elektronikus dokumentum] / |c Molnár Lajos |
| 260 | |c 2021 | ||
| 300 | |a 28 | ||
| 490 | 0 | |a INTEGRAL EQUATIONS AND OPERATOR THEORY |v 93 No. 1 | |
| 520 | 3 | |a In this paper we consider some faithful representations of positive Hilbert space operators on structures of nonnegative real functions defined on the unit sphere of the Hilbert space in question. Those representations turn order relations between positive operators to order relations between real functions. Two of them turn the usual Löwner order between operators to the pointwise order between functions, another two turn the spectral order between operators to the same, pointwise order between functions. We investigate which algebraic operations those representations preserve, hence which kind of algebraic structure the representing functions have. We study the differences among the different representing functions of the same positive operator. Finally, we introduce a new complete metric (which corresponds naturally to two of those representations) on the set of all invertible positive operators and formulate a conjecture concerning the corresponding isometry group. | |
| 650 | 4 | |a Matematika | |
| 700 | 0 | 1 | |a Ramanantoanina Andriamanankasina |e aut |
| 856 | 4 | 0 | |u http://publicatio.bibl.u-szeged.hu/37372/1/OnFunctionalRepresentationsofPositiveHilbertSpaceOperators.pdf |z Dokumentum-elérés |